The Southern Ocean houses a diverse and productive community of organisms 1,2 . Unicellular eukaryotic diatoms are the main primary producers in this environment, where photosynthesis is limited by low concentrations of dissolved iron and large seasonal fluctuations in light, temperature and the extent of sea ice 3-7 . How diatoms have adapted to this extreme environment is largely unknown. Here we present insights into the genome evolution of a cold-adapted diatom from the Southern Ocean, Fragilariopsis cylindrus 8,9 , based on a comparison with temperate diatoms. We find that approximately 24.7 per cent of the diploid F. cylindrus genome consists of genetic loci with alleles that are highly divergent (15.1 megabases of the total genome size of 61.1 megabases). These divergent alleles were differentially expressed across environmental conditions, including darkness, low iron, freezing, elevated temperature and increased CO 2 . Alleles with the largest ratio of non-synonymous to synonymous nucleotide substitutions also show the most pronounced condition-dependent expression, suggesting a correlation between diversifying selection and allelic differentiation.

Phylogenetic networks are rooted, labelled directed acyclic graphswhich are commonly used to represent reticulate evolution. There is a close relationship between phylogenetic networks and multi-labelled trees (MUL-trees). Indeed, any phylogenetic network N can be “unfolded” to obtain a MUL-tree U(N) and, conversely, a MUL-tree T can in certain circumstances be “folded” to obtain aphylogenetic network F(T) that exhibits T. In this paper, we study properties of the operations U and F in more detail. In particular, we introduce the class of stable networks, phylogenetic networks N for which F(U(N)) is isomorphic to N, characterise such networks, and show that they are related to the well-known class of tree-sibling networks. We also explore how the concept of displaying a tree in a network N can be related to displaying the tree in the MUL-tree U(N). To do this, we develop aphylogenetic analogue of graph fibrations. This allows us to view U(N) as the analogue of the universal cover of a digraph, and to establish a close connection between displaying trees in U(N) and reconciling phylogenetic trees with networks.

Phylogenetic networks are a generalization of phylogenetic trees that are used to represent reticulate evolution. Unrooted phylogenetic networks form a special class of such networks, which naturally generalize unrooted phylogenetic trees. In this paper we define two operations on unrooted phylogenetic networks, one of which is a generalization of the well-known nearest-neighbor interchange (NNI) operation on phylogenetic trees. We show that any unrooted phylogenetic network can be transformed into any other such network using only these operations. This generalizes the well-known fact that any phylogenetic tree can be transformed into any other such tree using only NNI operations. It also allows us to define a generalization of tree space and to define some new metrics on unrooted phylogenetic networks. To prove our main results, we employ some fascinating new connections between phylogenetic networks and cubic graphs that we have recently discovered. Our results should be useful in developing new strategies to search for optimal phylogenetic networks, a topic that has recently generated some interest in the literature, as well as for providing new ways to compare networks.

Phylogenetic networks are a generalization of evolutionary or phylogenetic trees that are used to represent the evolution of species which have undergone reticulate evolution. In this paper we consider spaces of such networks defined by some novel local operations that we introduce for converting one phylogenetic network into another. These operations are modeled on the well-studied nearest-neighbor interchange (NNI) operations on phylogenetic trees, and lead to natural generalizations of the tree spaces that have been previously associated to such operations. We present several results on spaces of some relatively simple networks, called level-1 networks, including the size of the neighborhood of a fixed network, and bounds on the diameter of the metric defined by taking the smallest number of operations required to convert one network into another. We expect that our results will be useful in the development of methods for systematically searching for optimal phylogenetic networks using, for example, likelihood and Bayesian approaches.